We are considering using a BMD cards in an upcoming Windows 10 based system which requires low latency.

In one mode, video comes in from either 3G SDI or 1080p60 on DVI. We are flexible which is preferable, and only one need format need be supported. We need to display the data with minimum latency on a monitor, while simultaneously acquiring to disk, possibly at a lower frame rate. In this mode, there is no additional processing or overlay of the video - just unmodified video in to video out.

In a second mode, the same monitor needs to act as an ordinary computer display, including displaying of the previously acquired video. Latency is not important in this mode.

What would be the best solution to provide minimum latency for the first mode?What is the minimum achievable latency at 60 fps?

Probably not the answer you are looking for, but hardware may be a much better way to solve this problem. If you get a simple HDMI or SDI matrix you can route the camera directly to the monitor as well as to the input of your capture card. When it is time for playback you can route the computer output, or the output of the decklink directly to the monitor. This way you get no extra delay at all. Getting the whole desktop out the decklink will be a pain anyway (unless you just want the recorded video full screen, not "In a second mode, the same monitor needs to act as an ordinary computer display, including displaying of the previously acquired video. Latency is not important in this mode."

As long as your card has output it is doable, but an RS232 controlled matrix, or video hub will make this faster and simpler.